Computer Methods in Applied Mechanics and Engineering, 2006
The paper describes the development and application of a combined discrete finite element scheme ... more The paper describes the development and application of a combined discrete finite element scheme to simulate the flow and compaction of irregular randomly packed particles to form a tabletted product. The techniques which have been adopted to achieve computational efficiency are described. These include contact detection, particle level deformation analysis and the presentation of results via a homogenisation strategy.The computing scheme in question is validated against published data and is shown to be capable of simulating the expected trends associated with the effects of particle shape, size and friction on the flow rate. The flow simulations also exhibit noticeable differences when compared with a geometric packing model. Over the relevant compaction regime, for which elastic behaviour is applicable, the present scheme also compares well with published work that uses a distinct element simulation approach and with experimental data. The advantage of the current scheme is the flexibility that it offers to capture a mixture of material properties and particle shape and that no restrictions are necessary on the contact models since these are integral in the calculation procedures.
Mathematical models of compaction in sedimentary basins typically assume a relationship between e... more Mathematical models of compaction in sedimentary basins typically assume a relationship between effective pressure pe and porosity ϕ, which is of a non-linear type; that is, pe = pe(ϕ). However, at depths greater than a kilometer, pressure solution becomes important and this relationship approaches a viscous one. We derive a mathematical model for viscous compaction in sedimentary basins and show how the model suggests different styles of behavior in the limits of slow and fast compaction.
The right choice of an optimization algorithm can be crucially important in finding the right sol... more The right choice of an optimization algorithm can be crucially important in finding the right solutions for a given optimization problem. There exist a diverse range of algorithms for optimization, including gradient-based algorithms, derivative-free algorithms and metaheuristics. Modern metaheuristic algorithms are often nature-inspired, and they are suitable for global optimization. In this chapter, we will briefly introduce optimization algorithms such as hill-climbing, trust-region method, simulated annealing, differential evolution, particle swarm optimization, harmony search, firefly algorithm and cuckoo search.
In modelling sediment compaction and mineral reactions, the rheological behaviour of sediments is... more In modelling sediment compaction and mineral reactions, the rheological behaviour of sediments is typically considered as poroelastic or purely viscous. In fact, compaction due to pressure solution and mechanical processes in porous media is far more complicated. A generalised model of viscoelastic compaction and the smectite to illite mineral reaction in hydrocarbon basins is presented. A one-step dehydration model of the mineral reaction is assumed. The obtained nonlinear governing equations are solved numerically and different combinations of physical parameters are used to simulate realistic situations in typical sedimentary basins. Comparison of numerical simulations with real data has shown very good agreement with respect to both the porosity profile and the mineral reaction.
For many data approximation problems in metrology, there are a num- ber of competing models which... more For many data approximation problems in metrology, there are a num- ber of competing models which can potentially fit the observed data. A crucial task is to quantify the extent to which one model performs better than others, taking into account the influence of random effects associated with the data. For example, for a given data set, we can use a series of polynomials of various degrees to fit the data using a least squares criterion. The residual sum of squares is a measure of how well the model fits the data. However, it is generally required to balance goodness of fit with minimising the model complexity. We consider a number of criteria that aim to do this: the Akaike information criterion (AIC), the Bayesian/Schwarz in- formation criterion, and the AIC with a correction for small sample size (AICc). In this paper, we compare the performance of these criteria for polynomial regression and show that for the examples tested the AICc criterion performs best. A second element of model selection is to determine from a set of feature vectors, the sub- set that defines a model space most suitable for describing the observed response. Since there are 2N possible model spaces defined by N feature vectors, for even a modest number of feature vectors it is necessary to reduce or prioritise the number of candidate models. Partial least squares and the least angle regression algorithms can be used as model reduction tools. We describe these algorithms in the context of feature selection and how they can be used with a model selection criterion such as AICc and illustrate their performance using simulations and on an application from human sensory perception.
Modelling and Simulation in Materials Science and Engineering, 2003
... Sci. Eng. 11 (2003) 321329 PII: S0965-0393(03)60418-3 Turing pattern formation of catalytic ... more ... Sci. Eng. 11 (2003) 321329 PII: S0965-0393(03)60418-3 Turing pattern formation of catalytic reactiondiffusion systems in engineering applications Xin-She Yang Faculty of Engineering, University of Wales Swansea, Swansea SA2 8PP, UK E-mail: xsyang@swansea.ac.uk ...
Compactional flow and temperature evolution in porous media is modelled as a two-phase deformatio... more Compactional flow and temperature evolution in porous media is modelled as a two-phase deformation process. The mathematical model leads to a pair of nonlinear diffusion equations with a moving boundary. Two distinguished features of density-driven compaction and temperature profile are then analysed and different styles of behaviour are compared and shown in this paper.
Mathematical modelling is becoming crucially important for earth sciences because the modelling o... more Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).
Enzyme reactions with inhibition and cooperativity are common in biological systems. A theoretica... more Enzyme reactions with inhibition and cooperativity are common in biological systems. A theoretical model for competitive and cooperative enzyme activity is formulated in terms of a pair of coupled nonlinear reaction-diffusion equations so as to derive the corresponding rule-based algorithm and nature-derived updating algorithms. A new stochastic cellular automaton is then constructed to simulate this nonlinear system. Numerical simulations show stable 2-D and 3-D pattern formation, and complex patterns have the interesting feature of self-organized criticality.
There exists a paradox in dip moveout (DMO) in seismic data processing. The paradox is why Notfor... more There exists a paradox in dip moveout (DMO) in seismic data processing. The paradox is why Notfors and Godfrey's approximate time log-stretched DMO can produce better impulse responses than the full log DMO, and why Hale's f-k DMO is correct although it was based on two inaccurate assumptions for the midpoint repositioning and the DMO time relationship? Based on the asymptotic analysis of the DMO algorithms, we find that any form of correctly formulated DMO must handle both space and time coordinates properly in order to deal with all dips accurately. The surprising improvement of Notfors and Godfrey's log DMO on Bale and Jakubowicz's full log DMO was due to the equivalent midpoint repositioning by transforming the time-related phase shift to the space-related phase shift. The explanation of why Hale's f-k DMO is correct although it was based on two inaccurate assumptions is that the two approximations exactly cancel each other in the f-k domain to give the correct final result.
A common but challenging task in modelling geophysical and geological processes is to handle mass... more A common but challenging task in modelling geophysical and geological processes is to handle massive data and to minimize certain objectives. This can essentially be considered as an optimization problem, and thus many new efficient metaheuristic optimization algorithms can be used. In this paper, we will introduce some modern metaheuristic optimization algorithms such as genetic algorithms, harmony search, firefly algorithm, particle swarm optimization and simulated annealing. We will also discuss how these algorithms can be applied to various applications in earth sciences, including nonlinear least-squares, support vector machine, Kriging, inverse finite element analysis, and data-mining. We will present a few examples to show how different problems can be reformulated as optimization. Finally, we will make some recommendations for choosing various algorithms to suit various problems. References 1) D. H. Wolpert and W. G. Macready, No free lunch theorems for optimization, IEEE Trans. Evolutionary Computation, Vol. 1, 67-82 (1997). 2) X. S. Yang, Nature-Inspired Metaheuristic Algorithms, Luniver Press, (2008). 3) X. S. Yang, Mathematical Modelling for Earth Sciences, Dunedin Academic Press, (2008).
Modelling crack propagation in fracture mechanics is a very challenging task. Different methods a... more Modelling crack propagation in fracture mechanics is a very challenging task. Different methods are usually robust under different conditions and there is no universally efficient numerical method for dynamic fracture simulations. Most available methods are computationally extensive and usually require frequent remeshing. This comparison study focuses on three major methods: the discrete element method, the adaptive fixed crack method and the element-free Galerkin method. By implementing these methods to study a 2D concrete beam with reinforcement of carbon-fibre reinforced polymer straps, we have shown that for simulations of a limited number of cracks, fixed crack method gives the best results. For multiple crossover cracks, the discrete element method is more suitable, while for moderate number of elements, the element-free Galerkin method are superior. However, for large number of elements, fixed crack method is most efficient. Comparisons will be given in details. In addition, new algorithms are still highly needed for the efficient simulations of dynamic crack propagations.
Computational optimization is becoming increasingly important in engineering design and industria... more Computational optimization is becoming increasingly important in engineering design and industrial applications. Products and services are often concerned with the maximization of profits and reduction of cost, but also aim at being more energy-efficient, environment-friendly and safety-ensured; at the same time they are limited by resources, time and money. This second workshop on Computational Optimization, Modelling and Simulation (COMS 2011) at ICCS 2011 will further summarize the latest developments of optimization and modelling and their applications in science, engineering and industry.
International Journal of Parallel, Emergent and Distributed Systems, 2012
We analyse the results of our experimental laboratory approximation of motorway networks with sli... more We analyse the results of our experimental laboratory approximation of motorway networks with slime mould Physarum polycephalum. Motorway networks of 14 geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, the Netherlands, UK and USA. For each geographical entity, we represented major urban areas by oat flakes and inoculated the slime mould in a capital. After slime mould spanned all urban areas with a network of its protoplasmic tubes, we extracted a generalised Physarum graph from the network and compared the graphs with an abstract motorway graph using most common measures. The measures employed are the number of independent cycles, cohesion, shortest paths lengths, diameter, the Harary index and the Randić index. We obtained a series of intriguing results, and found that the slime mould approximates best of all the motorway graphs of Belgium, Canada and China, and that for all entities studied the best match between Physarum and motorway graphs is detected by the Randić index (molecular branching index).
Livre: Computational optimization, methods and algorithms (series: studies in computational intel... more Livre: Computational optimization, methods and algorithms (series: studies in computational intelligence) KOZIEL Slawomir, YANG Xin-She.
Computer Methods in Applied Mechanics and Engineering, 2006
The paper describes the development and application of a combined discrete finite element scheme ... more The paper describes the development and application of a combined discrete finite element scheme to simulate the flow and compaction of irregular randomly packed particles to form a tabletted product. The techniques which have been adopted to achieve computational efficiency are described. These include contact detection, particle level deformation analysis and the presentation of results via a homogenisation strategy.The computing scheme in question is validated against published data and is shown to be capable of simulating the expected trends associated with the effects of particle shape, size and friction on the flow rate. The flow simulations also exhibit noticeable differences when compared with a geometric packing model. Over the relevant compaction regime, for which elastic behaviour is applicable, the present scheme also compares well with published work that uses a distinct element simulation approach and with experimental data. The advantage of the current scheme is the flexibility that it offers to capture a mixture of material properties and particle shape and that no restrictions are necessary on the contact models since these are integral in the calculation procedures.
Mathematical models of compaction in sedimentary basins typically assume a relationship between e... more Mathematical models of compaction in sedimentary basins typically assume a relationship between effective pressure pe and porosity ϕ, which is of a non-linear type; that is, pe = pe(ϕ). However, at depths greater than a kilometer, pressure solution becomes important and this relationship approaches a viscous one. We derive a mathematical model for viscous compaction in sedimentary basins and show how the model suggests different styles of behavior in the limits of slow and fast compaction.
The right choice of an optimization algorithm can be crucially important in finding the right sol... more The right choice of an optimization algorithm can be crucially important in finding the right solutions for a given optimization problem. There exist a diverse range of algorithms for optimization, including gradient-based algorithms, derivative-free algorithms and metaheuristics. Modern metaheuristic algorithms are often nature-inspired, and they are suitable for global optimization. In this chapter, we will briefly introduce optimization algorithms such as hill-climbing, trust-region method, simulated annealing, differential evolution, particle swarm optimization, harmony search, firefly algorithm and cuckoo search.
In modelling sediment compaction and mineral reactions, the rheological behaviour of sediments is... more In modelling sediment compaction and mineral reactions, the rheological behaviour of sediments is typically considered as poroelastic or purely viscous. In fact, compaction due to pressure solution and mechanical processes in porous media is far more complicated. A generalised model of viscoelastic compaction and the smectite to illite mineral reaction in hydrocarbon basins is presented. A one-step dehydration model of the mineral reaction is assumed. The obtained nonlinear governing equations are solved numerically and different combinations of physical parameters are used to simulate realistic situations in typical sedimentary basins. Comparison of numerical simulations with real data has shown very good agreement with respect to both the porosity profile and the mineral reaction.
For many data approximation problems in metrology, there are a num- ber of competing models which... more For many data approximation problems in metrology, there are a num- ber of competing models which can potentially fit the observed data. A crucial task is to quantify the extent to which one model performs better than others, taking into account the influence of random effects associated with the data. For example, for a given data set, we can use a series of polynomials of various degrees to fit the data using a least squares criterion. The residual sum of squares is a measure of how well the model fits the data. However, it is generally required to balance goodness of fit with minimising the model complexity. We consider a number of criteria that aim to do this: the Akaike information criterion (AIC), the Bayesian/Schwarz in- formation criterion, and the AIC with a correction for small sample size (AICc). In this paper, we compare the performance of these criteria for polynomial regression and show that for the examples tested the AICc criterion performs best. A second element of model selection is to determine from a set of feature vectors, the sub- set that defines a model space most suitable for describing the observed response. Since there are 2N possible model spaces defined by N feature vectors, for even a modest number of feature vectors it is necessary to reduce or prioritise the number of candidate models. Partial least squares and the least angle regression algorithms can be used as model reduction tools. We describe these algorithms in the context of feature selection and how they can be used with a model selection criterion such as AICc and illustrate their performance using simulations and on an application from human sensory perception.
Modelling and Simulation in Materials Science and Engineering, 2003
... Sci. Eng. 11 (2003) 321329 PII: S0965-0393(03)60418-3 Turing pattern formation of catalytic ... more ... Sci. Eng. 11 (2003) 321329 PII: S0965-0393(03)60418-3 Turing pattern formation of catalytic reactiondiffusion systems in engineering applications Xin-She Yang Faculty of Engineering, University of Wales Swansea, Swansea SA2 8PP, UK E-mail: xsyang@swansea.ac.uk ...
Compactional flow and temperature evolution in porous media is modelled as a two-phase deformatio... more Compactional flow and temperature evolution in porous media is modelled as a two-phase deformation process. The mathematical model leads to a pair of nonlinear diffusion equations with a moving boundary. Two distinguished features of density-driven compaction and temperature profile are then analysed and different styles of behaviour are compared and shown in this paper.
Mathematical modelling is becoming crucially important for earth sciences because the modelling o... more Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).
Enzyme reactions with inhibition and cooperativity are common in biological systems. A theoretica... more Enzyme reactions with inhibition and cooperativity are common in biological systems. A theoretical model for competitive and cooperative enzyme activity is formulated in terms of a pair of coupled nonlinear reaction-diffusion equations so as to derive the corresponding rule-based algorithm and nature-derived updating algorithms. A new stochastic cellular automaton is then constructed to simulate this nonlinear system. Numerical simulations show stable 2-D and 3-D pattern formation, and complex patterns have the interesting feature of self-organized criticality.
There exists a paradox in dip moveout (DMO) in seismic data processing. The paradox is why Notfor... more There exists a paradox in dip moveout (DMO) in seismic data processing. The paradox is why Notfors and Godfrey's approximate time log-stretched DMO can produce better impulse responses than the full log DMO, and why Hale's f-k DMO is correct although it was based on two inaccurate assumptions for the midpoint repositioning and the DMO time relationship? Based on the asymptotic analysis of the DMO algorithms, we find that any form of correctly formulated DMO must handle both space and time coordinates properly in order to deal with all dips accurately. The surprising improvement of Notfors and Godfrey's log DMO on Bale and Jakubowicz's full log DMO was due to the equivalent midpoint repositioning by transforming the time-related phase shift to the space-related phase shift. The explanation of why Hale's f-k DMO is correct although it was based on two inaccurate assumptions is that the two approximations exactly cancel each other in the f-k domain to give the correct final result.
A common but challenging task in modelling geophysical and geological processes is to handle mass... more A common but challenging task in modelling geophysical and geological processes is to handle massive data and to minimize certain objectives. This can essentially be considered as an optimization problem, and thus many new efficient metaheuristic optimization algorithms can be used. In this paper, we will introduce some modern metaheuristic optimization algorithms such as genetic algorithms, harmony search, firefly algorithm, particle swarm optimization and simulated annealing. We will also discuss how these algorithms can be applied to various applications in earth sciences, including nonlinear least-squares, support vector machine, Kriging, inverse finite element analysis, and data-mining. We will present a few examples to show how different problems can be reformulated as optimization. Finally, we will make some recommendations for choosing various algorithms to suit various problems. References 1) D. H. Wolpert and W. G. Macready, No free lunch theorems for optimization, IEEE Trans. Evolutionary Computation, Vol. 1, 67-82 (1997). 2) X. S. Yang, Nature-Inspired Metaheuristic Algorithms, Luniver Press, (2008). 3) X. S. Yang, Mathematical Modelling for Earth Sciences, Dunedin Academic Press, (2008).
Modelling crack propagation in fracture mechanics is a very challenging task. Different methods a... more Modelling crack propagation in fracture mechanics is a very challenging task. Different methods are usually robust under different conditions and there is no universally efficient numerical method for dynamic fracture simulations. Most available methods are computationally extensive and usually require frequent remeshing. This comparison study focuses on three major methods: the discrete element method, the adaptive fixed crack method and the element-free Galerkin method. By implementing these methods to study a 2D concrete beam with reinforcement of carbon-fibre reinforced polymer straps, we have shown that for simulations of a limited number of cracks, fixed crack method gives the best results. For multiple crossover cracks, the discrete element method is more suitable, while for moderate number of elements, the element-free Galerkin method are superior. However, for large number of elements, fixed crack method is most efficient. Comparisons will be given in details. In addition, new algorithms are still highly needed for the efficient simulations of dynamic crack propagations.
Computational optimization is becoming increasingly important in engineering design and industria... more Computational optimization is becoming increasingly important in engineering design and industrial applications. Products and services are often concerned with the maximization of profits and reduction of cost, but also aim at being more energy-efficient, environment-friendly and safety-ensured; at the same time they are limited by resources, time and money. This second workshop on Computational Optimization, Modelling and Simulation (COMS 2011) at ICCS 2011 will further summarize the latest developments of optimization and modelling and their applications in science, engineering and industry.
International Journal of Parallel, Emergent and Distributed Systems, 2012
We analyse the results of our experimental laboratory approximation of motorway networks with sli... more We analyse the results of our experimental laboratory approximation of motorway networks with slime mould Physarum polycephalum. Motorway networks of 14 geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, the Netherlands, UK and USA. For each geographical entity, we represented major urban areas by oat flakes and inoculated the slime mould in a capital. After slime mould spanned all urban areas with a network of its protoplasmic tubes, we extracted a generalised Physarum graph from the network and compared the graphs with an abstract motorway graph using most common measures. The measures employed are the number of independent cycles, cohesion, shortest paths lengths, diameter, the Harary index and the Randić index. We obtained a series of intriguing results, and found that the slime mould approximates best of all the motorway graphs of Belgium, Canada and China, and that for all entities studied the best match between Physarum and motorway graphs is detected by the Randić index (molecular branching index).
Livre: Computational optimization, methods and algorithms (series: studies in computational intel... more Livre: Computational optimization, methods and algorithms (series: studies in computational intelligence) KOZIEL Slawomir, YANG Xin-She.
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